Topology (What is a Topology?)
What is a Topology? Here is an introduction to one of the main areas in mathematics - Topology. #topology Some of the links below are affiliate links. As an Amazon Associate I earn from qualifying purchases. If you purchase through these links, it won't cost you any additional cash, b
From playlist Topology
I define closed sets, an important notion in topology and analysis. It is defined in terms of limit points, and has a priori nothing to do with open sets. Yet I show the important result that a set is closed if and only if its complement is open. More topology videos can be found on my pla
From playlist Topology
In this video, I introduce the order topology and prove that it is Hausdorff. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Topology
Topology 1.7 : More Examples of Topologies
In this video, I introduce important examples of topologies I didn't get the chance to get to. This includes The discrete and trivial topologies, subspace topology, the lower-bound and K topologies on the reals, the dictionary order, and the line with two origins. I also introduce (again)
From playlist Topology
In this video, I define connectedness, which is a very important concept in topology and math in general. Essentially, it means that your space only consists of one piece, whereas disconnected spaces have two or more pieces. I also define the related notion of path-connectedness. Topology
From playlist Topology
David Corwin, Kim's conjecture and effective Faltings
VaNTAGe seminar, on Nov 24, 2020 License: CC-BY-NC-SA.
From playlist ICERM/AGNTC workshop updates
Topology 1.1 : Open Sets of Reals
In this video, I give a definition of the open sets on the real numbers. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Topology
Topology 1.3 : Basis for a Topology
In this video, I define what a basis for a topology is. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Topology
Rational points and fundamental groups. - Ellenberg - Workshop 2 - CEB T2 2019
Jordan Ellenberg (University of Wisconsin-Madison) / 25.06.2019 Rational points and fundamental groups. I will talk about some results old and new about the relationship between rational points on varieties and fundamental groups. In a paper with Hast, we extend the class of curves to w
From playlist 2019 - T2 - Reinventing rational points
Nicolás Matte Bon: Confined subgroups and high transitivity
A subgroup of a group is confined if the closure of its conjugacy class in the Chabauty space does not contain the trivial subgroup. Such subgroups arise naturally as stabilisers for non-free actions on compact spaces. I will explain a result establishing a relation between the confined su
From playlist Dynamical Systems and Ordinary Differential Equations
Jacob Tsimerman, Unlikely intersections and the André-Oort conjecture
VaNTAGe Seminar, December 7, 2021 License: CC-BY-NC-SA
From playlist Complex multiplication and reduction of curves and abelian varieties
Jean-Louis Koszul - Interview à l'occasion des 50 ans du bâtiment de l'Institut Fourier
Jean-louis Koszul accompagné de Jacques Gasqui Aux questions : Ariane Rolland (CNRS) et Romain Vanel (CNRS) A l'image : Fanny Bastien (CNRS)
From playlist 50 ans du bâtiment Institut Fourier
Topology 1.4 : Product Topology Introduction
In this video, I define the product topology, and introduce the general cartesian product. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Topology
The Chabauty Topology 2 (Lecture-1) by Ian Biringer
PROGRAM: PROBABILISTIC METHODS IN NEGATIVE CURVATURE (ONLINE) ORGANIZERS: Riddhipratim Basu (ICTS - TIFR, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Mahan M J (TIFR, Mumbai) DATE & TIME: 01 March 2021 to 12 March 2021 VENUE: Online Due to the ongoing COVID pandemic, the meeting will
From playlist Probabilistic Methods in Negative Curvature (Online)
Nicholas Triantafillou, Computing isolated points on modular curves
VaNTAGe seminar, on Nov 10, 2020 License: CC-BY-NC-SA.
From playlist ICERM/AGNTC workshop updates
Jeremy Rouse, l-adic images of Galois for elliptic curves over Q
VaNTAGe seminar, June 22, 2021 License: CC-BY-NC-SA
From playlist Modular curves and Galois representations
Here is one of the most important curves in mathematics. It is an example of a set that is connected, but not path-connected, and is very prominent in topology and analysis. Topology Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmA13vj9xkHGGBXRMV32EKVI Subscribe to my channel
From playlist Topology
Gluing is a good method to construct new topological spaces from known ones. Here a rectangles is glued along the edges to form a torus. Often the fundamental group of the glued object can be calculated from the pieces (here a rectangles) and the glue (here two intersecting circles). Th
From playlist Algebraic Topology
Ishai Dan Cohen:The polylog quotient and the Goncharov quotient in computational Chabauty-Kim theory
Abstract: Polylogarithms are those multiple polylogarithms which factor through a certain quotient of the de Rham fundamental group of the thrice punctured line known as the polylogarithmic quotient. In joint work with David Corwin, building on work that was partially joint with Stefan We
From playlist HIM Lectures: Trimester Program "Periods in Number Theory, Algebraic Geometry and Physics"